Freezing-Induced Interaction Engineering

• Freezing-induced interaction engineering is a strategy that employs controlled phase transitions to tailor effective interactions across various systems.
• It harnesses mechanisms such as cryoconcentration, interfacial-energy modulation, and dynamical projection to modify local thermodynamic and transport properties.
• Applications range from self-assembly in block-copolymer systems to interaction suppression in quantum and spin platforms, highlighting its wide practical impact.

Searching arXiv for the cited papers and the topic to ground the article in current arXiv records. {"^^^^^^^^4query4 interaction engineering\"^^^^^^^^4 OR ti:\4^^^^^^^^"Freezing-induced\" OR abs:\4^^^^^^^^"freezing-induced interaction engineering\"","max_results":^^^^4all:\4query4^^^^,"sort_by":"submittedDate","sort_order":"descending"} {"^^^^^^^^4query4 OR (&&&^^^^4all:\4^^^^&&&) OR (&&&^^^^4 OR ti:\4^^^^&&&)","max_results":5,"sort_by":"relevance","sort_order":"descending"} Freezing-induced interaction engineering denotes the use of freezing, freezing-like dynamical arrest, or freezing-controlled state selection to reshape effective interactions, concentration fields, and accessible dynamical subspaces. In the literature represented here, the term covers several distinct but structurally related mechanisms: progressive freezing-induced concentration in block-copolymer/silica systems, adsorption-controlled inhibition of ice growth by antifreeze proteins, premelting-mediated control of cell–ice interactions, localized freezing that switches droplet wetting states on textured surfaces, solute-mediated long-range interactions ahead of solidification fronts, and interaction-induced freezing in quantum-spin platforms (&&&^^^^4query4^^^^&&&). Across these settings, freezing acts not merely as a terminal phase transition but as a control variable that redistributes matter, renormalizes local thermodynamic driving forces, modifies transport, or projects coupled degrees of freedom into reduced effective dynamics.

^^^^4all:\4^^^^. Conceptual scope and recurring mechanisms

A recurrent pattern across the cited works is that freezing changes interactions indirectly by altering the environment in which those interactions are realized. In soft-matter and interfacial systems, solidification rejects solutes, changes local composition, perturbs pH, broadens or thins premelted films, and modifies curvature and heat flux. In quantum and magnetic settings, “freezing” instead refers to dynamical confinement or local spin freezing that suppresses transitions and thereby exposes or reweights particular interaction channels (Krithika et al., 2020).

Several mechanistic classes recur. One class is cryoconcentration: as ice forms, species with extremely low solubility in the crystal are expelled into the remaining liquid, so local concentration follows the standard relation

PRESERVED_PLACEHOLDER_^^^^4query4^^^^

where PRESERVED_PLACEHOLDER_^^^^4all:\4^^^^ is the local ice volume fraction. This framework is explicit in freezing-induced self-assembly of block-copolymer micelles and silica oligomers, where concentration growth drives ordering below PRESERVED_PLACEHOLDER_^^^^4 OR ti:\4^^^^ (&&&^^^^4query4^^^^&&&). A second class is interfacial-energy engineering, where adsorption or premelting modifies the free-energy cost of interfaces. In antifreeze-protein models, the interfacial surface tension decreases as

PRESERVED_PLACEHOLDER_^^^^4 OR abs:\4^^^^

while the diffuse interface thickness increases as $\delta\sim(\sqrt{\aleph/2})^{-1}$, which suppresses coarsening and locks grain size (&&&^^^^4 OR ti:\4^^^^&&&). A third class is front-mediated transport and rejection, where a moving interface induces long-range interactions via concentration gradients or isotherm distortion, as in freezing emulsions and the frozen Cheerios effect (Dedovets et al., 2017). A fourth class is dynamical projection, where a strongly driven auxiliary degree of freedom is frozen in a dressed state and its projection renormalizes the Hamiltonian of the remaining subsystem, enabling interaction-on and interaction-off regimes without changing native couplings (Xie et al., 18 May 2026).

This suggests a unifying interpretation: freezing-induced interaction engineering is less a single method than a family of strategies in which freezing, or dynamical freezing, converts latent thermodynamic structure into controllable effective interactions.

^^^^4 OR ti:\4^^^^. Progressive freezing-induced concentration and self-assembly

The clearest soft-matter realization is the freezing-induced self-assembly of P^^^^4all:\4 OR ti:\4 OR abs:\4^^^^-templated silica. In that system, Pluronic P^^^^4all:\4 OR ti:\4 OR abs:\4^^^^, a triblock copolymer $$(\mathrm{EO})_{20}(\mathrm{PO})_{70}(\mathrm{EO})_{20}$$, is dissolved in water below $35\,^{\circ}\mathrm{C}$; the solution pH is adjusted between ^^^^4all:\4^^^^.^^^^4all:\4^^^^ and ^^^^4all:\4^^^^.8 using HCl; TEOS is added to give a final molar composition $1\,\mathrm{SiO_2}:71$–$83\,\mathrm{H_2O}:0.017\,\mathrm{P123}$; the mixture is aged for ^^^^4 OR abs:\4^^^^ h below $35\,^{\circ}\mathrm{C}$; ethanol formed during hydrolysis is removed by rotary evaporation; directional freezing is then performed at PRESERVED_PLACEHOLDER_^^^^4all:\4query4^^^^; freeze-drying removes ice; and calcination at PRESERVED_PLACEHOLDER_^^^^4all:\4all:\4^^^^ for 4 h at PRESERVED_PLACEHOLDER_^^^^4all:\4 OR ti:\4^^^^ removes P^^^^4all:\4 OR ti:\4 OR abs:\4^^^^ and consolidates the silica framework (&&&^^^^4query4^^^^&&&).

The proposed mechanism is progressive freezing-induced concentration, abbreviated PFIC in the source material. As water crystallizes, P^^^^4all:\4 OR ti:\4 OR abs:\4^^^^ micelles or aggregates, hydrolyzed silica oligomers, and HCl are rejected into the interstitial liquid, which progressively raises their local concentrations. The paper quantitatively estimates that HCl rejection lowers the local pH from ^^^^4all:\4^^^^.^^^^4 OR abs:\4^^^^ to approximately ^^^^4all:\4^^^^.^^^^4query4^^^^ in the unfrozen liquid. This acidification, combined with concentration increase, alters EO-block hydration, PO-block solvophobicity, silica–surfactant hydrogen bonding, and effective micelle–micelle interactions. Although P^^^^4all:\4 OR ti:\4 OR abs:\4^^^^ micelles typically form between PRESERVED_PLACEHOLDER_^^^^4all:\4 OR abs:\4^^^^ and PRESERVED_PLACEHOLDER_^^^^4all:\44^^^^ and surfactants rarely form lyotropic mesophases below PRESERVED_PLACEHOLDER_^^^^4all:\4^^^^5, PFIC drives the system across an ordering threshold and produces a ^^^^4 OR ti:\4^^^^D hexagonal mesophase with p6mm symmetry (&&&^^^^4query4^^^^&&&).

The transport picture is described by standard moving-front relations,

PRESERVED_PLACEHOLDER_^^^^4all:\4^^^^6

PRESERVED_PLACEHOLDER_^^^^4all:\4^^^^7

and, where relevant,

PRESERVED_PLACEHOLDER_^^^^4all:\4^^^^8

The Peclet number PRESERVED_PLACEHOLDER_^^^^4all:\4^^^^9 distinguishes advective solute rejection from diffusive relaxation. The paper does not report PRESERVED_PLACEHOLDER_^^^^4 OR ti:\4query4^^^^, PRESERVED_PLACEHOLDER_^^^^4 OR ti:\4all:\4^^^^, PRESERVED_PLACEHOLDER_^^^^4 OR ti:\4 OR ti:\4^^^^, or PRESERVED_PLACEHOLDER_^^^^4 OR ti:\4 OR abs:\4^^^^ numerically, but it uses this framework to connect front dynamics with sharpening of concentration gradients and orientational bias near the interface (&&&^^^^4query4^^^^&&&).

Structurally, PFIC yields a hierarchical architecture rather than a single ordered length scale. Straight directional macropores arise from ice growth, with mercury porosimetry and SEM showing macropore families at PRESERVED_PLACEHOLDER_^^^^4 OR ti:\44^^^^–PRESERVED_PLACEHOLDER_^^^^4 OR ti:\4^^^^5 and PRESERVED_PLACEHOLDER_^^^^4 OR ti:\4^^^^6–PRESERVED_PLACEHOLDER_^^^^4 OR ti:\4^^^^7. A secondary foam-like and bundle-like pore network perpendicular to the main macropores is also observed, with a secondary pore region about PRESERVED_PLACEHOLDER_^^^^4 OR ti:\4^^^^8 thick and bundle diameters of PRESERVED_PLACEHOLDER_^^^^4 OR ti:\4^^^^9–PRESERVED_PLACEHOLDER_^^^^4 OR abs:\4query4^^^^. TEM reveals ^^^^4 OR ti:\4^^^^D hexagonal ordering with pore-center spacing PRESERVED_PLACEHOLDER_^^^^4 OR abs:\4all:\4^^^^ and cell parameter PRESERVED_PLACEHOLDER_^^^^4 OR abs:\4 OR ti:\4^^^^, while small-angle X-ray diffraction shows three p6mm reflections at PRESERVED_PLACEHOLDER_^^^^4 OR abs:\4 OR abs:\4^^^^, PRESERVED_PLACEHOLDER_^^^^4 OR abs:\44^^^^, and PRESERVED_PLACEHOLDER_^^^^4 OR abs:\4^^^^5 indexed as (^^^^4all:\4query4^^^^), (^^^^4all:\4all:\4^^^^), and (^^^^4 OR ti:\4query4^^^^). Nitrogen sorption gives type IV isotherms with H^^^^4all:\4^^^^ hysteresis ending in H4 and mesopore sizes of PRESERVED_PLACEHOLDER_^^^^4 OR abs:\4^^^^6–PRESERVED_PLACEHOLDER_^^^^4 OR abs:\4^^^^7 (&&&^^^^4query4^^^^&&&).

A closely related transport-mediated mechanism appears in freezing emulsions. Five-dimensional confocal imaging of oil-in-water emulsions under directional freezing showed that solute rejection ahead of the interface creates a concentration boundary layer with enrichment factors of ^^^^4 OR abs:\4^^^^–^^^^4all:\4query4^^^^ relative to the bulk, over distances PRESERVED_PLACEHOLDER_^^^^4 OR abs:\4^^^^8 on the order of PRESERVED_PLACEHOLDER_^^^^4 OR abs:\4^^^^9, and droplet velocities up to about $\delta\sim(\sqrt{\aleph/2})^{-1}$^^^^4query4^^^^. The onset distance of droplet repulsion scales linearly with the onset distance of solute buildup, and the enriched solute field enhances premelting, reverses interface curvature near droplets, and drives long-range rearrangement prior to engulfment (Dedovets et al., 2017).

^^^^4 OR abs:\4^^^^. Premelting, adsorption, and interfacial-energy control

A second major branch of freezing-induced interaction engineering operates through premelting and adsorption, especially at ice–liquid and ice–solid interfaces. The antifreeze-protein model is the most explicit theoretical treatment. There, a Ginzburg–Landau/Cahn–Hilliard formulation uses an ice order parameter and an AFP concentration field to show that AFP–ice coupling lowers interfacial energy density and surface tension, broadens the diffuse interface, shrinks the spinodal freezing region, accelerates clustering of pre-ice embryos, and then arrests coarsening through grain-size locking (&&&^^^^4 OR ti:\4^^^^&&&).

The free-energy density is written with a coupling term of the form $\delta\sim(\sqrt{\aleph/2})^{-1}$^^^^4all:\4^^^^, and after rescaling one obtains coupled evolution equations for the order parameter $\delta\sim(\sqrt{\aleph/2})^{-1}$^^^^4 OR ti:\4^^^^ and the AFP concentration $\delta\sim(\sqrt{\aleph/2})^{-1}$^^^^4 OR abs:\4^^^^. Static solutions yield a kink profile

$\delta\sim(\sqrt{\aleph/2})^{-1}$4

with interfacial surface tension

$\delta\sim(\sqrt{\aleph/2})^{-1}$5

As AFP coupling increases, $\delta\sim(\sqrt{\aleph/2})^{-1}$6 decreases, so the interface broadens and the spinodal region collapses at the threshold $\delta\sim(\sqrt{\aleph/2})^{-1}$7 (&&&^^^^4 OR ti:\4^^^^&&&). Linear stability analysis likewise shows that AFPs shrink the unstable band of wave numbers. Simulations then show a characteristic two-stage behavior: faster clustering of embryos but earlier saturation at smaller grain size.

The same interfacial logic appears in premelting-directed design of cell–ice interactions. Nanoshells such as TA–Fe$\delta\sim(\sqrt{\aleph/2})^{-1}$8 coordination shells on mammalian cells and SiO$\delta\sim(\sqrt{\aleph/2})^{-1}$9 shells on yeast alter the effective Hamaker constant $$(\mathrm{EO})_{20}(\mathrm{PO})_{70}(\mathrm{EO})_{20}$$^^^^4query4^^^^ of the ice–water–shell–cell stack, thereby tuning the premelted film thickness $$(\mathrm{EO})_{20}(\mathrm{PO})_{70}(\mathrm{EO})_{20}$$^^^^4all:\4^^^^. Near equilibrium,

$$(\mathrm{EO})_{20}(\mathrm{PO})_{70}(\mathrm{EO})_{20}$$^^^^4 OR ti:\4^^^^

and when van der Waals forces dominate,

$$(\mathrm{EO})_{20}(\mathrm{PO})_{70}(\mathrm{EO})_{20}$$^^^^4 OR abs:\4^^^^

The study reports that coated cells directionally migrate toward the warm side in a thermal gradient $$(\mathrm{EO})_{20}(\mathrm{PO})_{70}(\mathrm{EO})_{20}$$4, whereas native cells are nearly immobile, and interprets this through a thermomolecular pressure gradient and thin-film lubrication. A lubrication-based estimate gives

$$(\mathrm{EO})_{20}(\mathrm{PO})_{70}(\mathrm{EO})_{20}$$5

so increasing $$(\mathrm{EO})_{20}(\mathrm{PO})_{70}(\mathrm{EO})_{20}$$6 thickens the film and accelerates migration (&&&^^^^4all:\4^^^^6&&&).

This interfacial engineering has direct consequences for freezing damage. Native mammalian cells were engulfed by a directional freezing front at about $$(\mathrm{EO})_{20}(\mathrm{PO})_{70}(\mathrm{EO})_{20}$$7, whereas coated cells were repelled at $$(\mathrm{EO})_{20}(\mathrm{PO})_{70}(\mathrm{EO})_{20}$$8 and $$(\mathrm{EO})_{20}(\mathrm{PO})_{70}(\mathrm{EO})_{20}$$9. After freezing at $35\,^{\circ}\mathrm{C}$^^^^4query4^^^^ for ^^^^4all:\44^^^^ h and directional thawing, viability was about ^^^^4all:\4^^^^7% for native cells and about ^^^^4 OR ti:\4^^^^7% for coated cells; after 7^^^^4 OR ti:\4^^^^ h, viability was about ^^^^4all:\4query4^^^^% and ^^^^4 OR ti:\4query4^^^^%, respectively (&&&^^^^4all:\4^^^^6&&&). The paper interprets these results as evidence that premelting modulation reduces mechanical damage during freezing and recrystallization during thawing.

The same emphasis on interfacial proximity appears in contact freezing. Molecular simulations of INP-supported nanofilms show that nanoscale proximity between an ice-nucleating particle and a free interface is sufficient to generate large kinetic enhancements, but only when the free interface itself has surface-freezing propensity. In the surface-freezing model SW^^^^4 OR ti:\4all:\4^^^^, reducing film thickness to about $35\,^{\circ}\mathrm{C}$^^^^4all:\4^^^^ produces hourglass-shaped critical nuclei that span the two interfaces and lower the nucleation barrier by $35\,^{\circ}\mathrm{C}$^^^^4 OR ti:\4^^^^ for graphene-supported films and $35\,^{\circ}\mathrm{C}$^^^^4 OR abs:\4^^^^ for a structureless wall. By contrast, mW, which lacks surface-freezing propensity, shows no systematic thickness dependence (&&&^^^^4all:\4^^^^8&&&). This directly links interface proximity to modified nucleation pathways rather than to transient collision effects alone.

4. Front-mediated morphology, wetting-state selection, and particle organization

Freezing-induced interaction engineering also appears as a means of selecting macroscopic morphology by controlling the competition between penetration, heat transfer, solidification, and front-mediated forces. On supercooled micro-patterned silicon with square micropillars of width $35\,^{\circ}\mathrm{C}$4, spacing $35\,^{\circ}\mathrm{C}$5, height $35\,^{\circ}\mathrm{C}$6, and solid fraction $35\,^{\circ}\mathrm{C}$7, localized freezing at the droplet base can arrest impalement and preserve a final Cassie state after impact. At fixed $35\,^{\circ}\mathrm{C}$8 and $35\,^{\circ}\mathrm{C}$9, decreasing $1\,\mathrm{SiO_2}:71$^^^^4query4^^^^ from $1\,\mathrm{SiO_2}:71$^^^^4all:\4^^^^ to $1\,\mathrm{SiO_2}:71$^^^^4 OR ti:\4^^^^ drives a transition from Wenzel to partial Wenzel to Cassie. At fixed $1\,\mathrm{SiO_2}:71$^^^^4 OR abs:\4^^^^, increasing $1\,\mathrm{SiO_2}:71$4 from about $1\,\mathrm{SiO_2}:71$5 to $1\,\mathrm{SiO_2}:71$6 drives the reverse transition from Cassie to Wenzel (&&&^^^^4all:\4^^^^9&&&).

The key criterion is the competition between freezing and impalement timescales. The study formulates this through

$1\,\mathrm{SiO_2}:71$7

and

$1\,\mathrm{SiO_2}:71$8

with

$1\,\mathrm{SiO_2}:71$9

A Cassie/Wenzel regime map in the $83\,\mathrm{H_2O}:0.017\,\mathrm{P123}$^^^^4query4^^^^ plane shows that Cassie retention requires low Weber number and high Stefan number. The experiments further show that the projected penetration-area fraction $83\,\mathrm{H_2O}:0.017\,\mathrm{P123}$^^^^4all:\4^^^^ decreases from about ^^^^4all:\4query4^^^^% at $83\,\mathrm{H_2O}:0.017\,\mathrm{P123}$^^^^4 OR ti:\4^^^^ to less than ^^^^4all:\4^^^^.5% at $83\,\mathrm{H_2O}:0.017\,\mathrm{P123}$^^^^4 OR abs:\4^^^^, while the dimensionless freezing time exhibits a nonmonotonic dependence on wall temperature (&&&^^^^4all:\4^^^^9&&&).

Front-mediated interactions can also act directly between suspended inclusions. In the frozen Cheerios effect, particles near an advancing water–ice interface experience lateral attraction or repulsion because thermal-conductivity mismatch distorts the isotherm, and the premelting-mediated repelling force acts normal to that distorted interface. For two particles, the lateral velocity component is

$83\,\mathrm{H_2O}:0.017\,\mathrm{P123}$4

For a spherical particle in a uniform thermal gradient, the far-field interface deflection simplifies to

$83\,\mathrm{H_2O}:0.017\,\mathrm{P123}$5

with $83\,\mathrm{H_2O}:0.017\,\mathrm{P123}$6. Hence $83\,\mathrm{H_2O}:0.017\,\mathrm{P123}$7 implies attraction, whereas $83\,\mathrm{H_2O}:0.017\,\mathrm{P123}$8 implies repulsion. Experimentally, glass spheres attract and cluster in water and DMSO, while polystyrene, PMMA, and silicone oil repel in water (&&&^^^^4 OR ti:\4all:\4^^^^&&&).

The efficacy of this interaction depends strongly on front velocity relative to the single-particle critical engulfment speed $83\,\mathrm{H_2O}:0.017\,\mathrm{P123}$9. Near $35\,^{\circ}\mathrm{C}$^^^^4query4^^^^, the interaction time and distance diverge as

$35\,^{\circ}\mathrm{C}$^^^^4all:\4^^^^

$35\,^{\circ}\mathrm{C}$^^^^4 OR ti:\4^^^^

whereas for $35\,^{\circ}\mathrm{C}$^^^^4 OR abs:\4^^^^ one has $35\,^{\circ}\mathrm{C}$4 (&&&^^^^4 OR ti:\4all:\4^^^^&&&). This gives a direct design rule: operate just above engulfment to maximize interaction time before particles are frozen in place.

At a larger scale, collective droplet freezing can itself become an interaction pathway. In supercooled droplet arrays at about ^^^^4 OR abs:\4^^^^ mbar, the first recalescing droplet generates a warm vapor bolus that diffuses with measured speed about $35\,^{\circ}\mathrm{C}$5, locally supersaturates the environment of neighboring droplets with $35\,^{\circ}\mathrm{C}$6, and triggers cascade freezing. For droplets spaced about $35\,^{\circ}\mathrm{C}$7 apart, the second droplet froze within about $35\,^{\circ}\mathrm{C}$8–$35\,^{\circ}\mathrm{C}$9 of the first, and an array of ten droplets froze within about PRESERVED_PLACEHOLDER_^^^^4all:\4query4query4^^^^ (&&&^^^^4 OR ti:\4 OR abs:\4^^^^&&&). This shows that freezing-induced interaction engineering can propagate through vapor-mediated coupling even when droplets are not in physical contact.

5. Freezing as a control primitive in magnetic and quantum systems

Outside classical solidification, the same logic appears in systems where “freezing” means arrested local dynamics. In the pyrochlore series PRESERVED_PLACEHOLDER_^^^^4all:\4query4all:\4^^^^, Eu substitution expands the lattice, increases nearest-neighbor separation, reduces the net effective moment, and changes the balance among exchange, dipolar, and single-ion terms. Across the series, a weak single-ion spin-freezing feature remains near PRESERVED_PLACEHOLDER_^^^^4all:\4query4 OR ti:\4^^^^–PRESERVED_PLACEHOLDER_^^^^4all:\4query4 OR abs:\4^^^^ at 5^^^^4query4query4^^^^ Hz, with Arrhenius activation energies from about PRESERVED_PLACEHOLDER_^^^^4all:\4query44^^^^ down to about PRESERVED_PLACEHOLDER_^^^^4all:\4query4^^^^5 and attempt frequencies on the order of PRESERVED_PLACEHOLDER_^^^^4all:\4query4^^^^6. The Mydosh parameter for PRESERVED_PLACEHOLDER_^^^^4all:\4query4^^^^7 is about ^^^^4query4^^^^.^^^^4 OR abs:\4^^^^6, far above canonical spin-glass values, so the reported freezing is interpreted as single-ion rather than collective glassiness (&&&^^^^4all:\4^^^^&&&).

Application of PRESERVED_PLACEHOLDER_^^^^4all:\4query4^^^^8 produces a field-induced transition at PRESERVED_PLACEHOLDER_^^^^4all:\4query4^^^^9 that shifts systematically upward with Eu content: about PRESERVED_PLACEHOLDER_^^^^4all:\4all:\4query4^^^^ for PRESERVED_PLACEHOLDER_^^^^4all:\4all:\4all:\4^^^^, PRESERVED_PLACEHOLDER_^^^^4all:\4all:\4 OR ti:\4^^^^ for PRESERVED_PLACEHOLDER_^^^^4all:\4all:\4 OR abs:\4^^^^, PRESERVED_PLACEHOLDER_^^^^4all:\4all:\44^^^^ for PRESERVED_PLACEHOLDER_^^^^4all:\4all:\4^^^^5, PRESERVED_PLACEHOLDER_^^^^4all:\4all:\4^^^^6 for PRESERVED_PLACEHOLDER_^^^^4all:\4all:\4^^^^7, and PRESERVED_PLACEHOLDER_^^^^4all:\4all:\4^^^^8 for PRESERVED_PLACEHOLDER_^^^^4all:\4all:\4^^^^9, with no PRESERVED_PLACEHOLDER_^^^^4all:\4 OR ti:\4query4^^^^ in PRESERVED_PLACEHOLDER_^^^^4all:\4 OR ti:\4all:\4^^^^. Because the Zeeman scale for fully polarizing TbPRESERVED_PLACEHOLDER_^^^^4all:\4 OR ti:\4 OR ti:\4^^^^ at ^^^^4all:\4^^^^ T is about PRESERVED_PLACEHOLDER_^^^^4all:\4 OR ti:\4 OR abs:\4^^^^, the transition is assigned to single-moment saturation (&&&^^^^4all:\4^^^^&&&). Here, “freezing-induced interaction engineering” is realized by chemical substitution and field control rather than by a phase front, but the operative principle is similar: freeze one sector of the dynamics to expose another.

The same principle is more explicit in quantum simulators. In NMR implementations of Rydberg blockade analogues, strong Ising-type couplings and unequal drive amplitudes confine dynamics to reduced subspaces. In the two-qubit experiment, PRESERVED_PLACEHOLDER_^^^^4all:\4 OR ti:\44^^^^ and PRESERVED_PLACEHOLDER_^^^^4all:\4 OR ti:\4^^^^5 satisfy the blockade criterion PRESERVED_PLACEHOLDER_^^^^4all:\4 OR ti:\4^^^^6, producing oscillations between PRESERVED_PLACEHOLDER_^^^^4all:\4 OR ti:\4^^^^7 and PRESERVED_PLACEHOLDER_^^^^4all:\4 OR ti:\4^^^^8 at PRESERVED_PLACEHOLDER_^^^^4all:\4 OR ti:\4^^^^9 with no detectable PRESERVED_PLACEHOLDER_^^^^4all:\4 OR abs:\4query4^^^^ population. With amplitude hierarchy PRESERVED_PLACEHOLDER_^^^^4all:\4 OR abs:\4all:\4^^^^ versus PRESERVED_PLACEHOLDER_^^^^4all:\4 OR abs:\4 OR ti:\4^^^^, the weakly driven qubit freezes and the dynamics become PRESERVED_PLACEHOLDER_^^^^4all:\4 OR abs:\4 OR abs:\4^^^^ or PRESERVED_PLACEHOLDER_^^^^4all:\4 OR abs:\44^^^^ depending on which drive is stronger (Krithika et al., 2020).

In NV centers, simultaneous drives on the electron and nuclear spins with unequal Rabi frequencies suppress nuclear dynamics through a dressed-state mechanism. In the rotating frame,

PRESERVED_PLACEHOLDER_^^^^4all:\4 OR abs:\4^^^^5

and when PRESERVED_PLACEHOLDER_^^^^4all:\4 OR abs:\4^^^^6, the oscillatory hyperfine terms average away. Simulations with PRESERVED_PLACEHOLDER_^^^^4all:\4 OR abs:\4^^^^7, PRESERVED_PLACEHOLDER_^^^^4all:\4 OR abs:\4^^^^8, and PRESERVED_PLACEHOLDER_^^^^4all:\4 OR abs:\4^^^^9 in the ^^^^4 OR ti:\4^^^^–4 MHz range show that the nuclear spin can be frozen against strong resonant or broadband RF noise, while quantum discord between electron and nuclear spins is strongly suppressed in the frozen regime (&&&^^^^4 OR ti:\4^^^^7&&&).

A related but more explicitly interaction-engineering use appears in a three-qubit drive-only architecture. There, a driven modulator qubit PRESERVED_PLACEHOLDER_^^^^4all:\44query4^^^^ is frozen in a dressed eigenstate, and its projected coupling to PRESERVED_PLACEHOLDER_^^^^4all:\44all:\4^^^^ renormalizes the dressed frequency of PRESERVED_PLACEHOLDER_^^^^4all:\44 OR ti:\4^^^^ relative to PRESERVED_PLACEHOLDER_^^^^4all:\44 OR abs:\4^^^^. The dressed splitting is PRESERVED_PLACEHOLDER_^^^^4all:\444^^^^ and the effective dressed-frame detuning can be tuned between large and near-zero values by the drive frequency alone. Full lab-frame simulations report interaction-off suppression ratio PRESERVED_PLACEHOLDER_^^^^4all:\44^^^^5 and interaction-on infidelity PRESERVED_PLACEHOLDER_^^^^4all:\44^^^^6 at the optimized point (Xie et al., 18 May 2026). This is a direct realization of freezing-induced interaction engineering in the narrow sense: freezing one subsystem projects and reshapes the effective Hamiltonian of the rest.

6. General design rules, limitations, and unresolved questions

Across these works, several design rules recur. First, freezing-induced interaction engineering generally requires that the freezing process outrun the relaxational process one aims to override. In PFIC, advective rejection must outpace diffusion sufficiently to push the system across an ordering threshold (&&&^^^^4query4^^^^&&&). In droplet impact, basal solidification must occur before penetration into the texture (&&&^^^^4all:\4^^^^9&&&). In contact freezing, nanoscale proximity matters only when the free interface itself enhances nucleation (&&&^^^^4all:\4^^^^8&&&). In frozen Cheerios interactions, front speed must be chosen relative to the critical engulfment speed so that particles remain near the interface long enough to drift laterally (&&&^^^^4 OR ti:\4all:\4^^^^&&&). In quantum versions, the freezing gap must exceed residual couplings and noise rates (&&&^^^^4 OR ti:\4^^^^7&&&).

Second, the operative control variable is often not a nominal bulk property but a local, dynamically generated one. In block-copolymer freezing it is the unfrozen interstitial composition and local pH, not the initial bath composition (&&&^^^^4query4^^^^&&&). In polymer-containing droplets it is spatially heterogeneous freeze-induced polymer segregation, not a homogeneous freezing-point shift, that explains tip blunting and bubble suppression (&&&^^^^4 OR abs:\4^^^^5&&&). In premelting-directed cryobiology it is the local effective Hamaker constant and film thickness, not merely shell presence, that controls migration and damage mitigation (&&&^^^^4all:\4^^^^6&&&). In contact freezing it is nanoscale interfacial spacing, not merely collision, that controls barrier lowering (&&&^^^^4all:\4^^^^8&&&).

Third, hierarchical or spatially nonuniform outcomes are typical rather than exceptional. FISA produces aligned mesopores near a macropore face and more random domains deeper in the wall (&&&^^^^4query4^^^^&&&). Freezing emulsions generate premelted films that later break into string-of-pearls structures under capillary instability (Dedovets et al., 2017). PVA-containing droplets retain polymer-rich domains both in the interior and at the surface after freezing (&&&^^^^4 OR abs:\4^^^^5&&&). This suggests that freezing-induced interaction engineering is intrinsically spatiotemporal: the same protocol can create distinct interaction regimes at different positions or times.

Several controversies and open questions remain. In the P^^^^4all:\4 OR ti:\4 OR abs:\4^^^^–silica system, it is unresolved whether micelles pre-exist before freezing or form during freezing, and whether ordering is completed during freezing or finalized upon thawing or aging (&&&^^^^4query4^^^^&&&). In contact freezing, the central dispute concerns the relative roles of contact-line effects, transient perturbations, and nanoscale interfacial proximity; the cited nanofilm study supports proximity as sufficient under the stated condition of surface-freezing propensity, but does not eliminate additional mechanisms in experiment (&&&^^^^4all:\4^^^^8&&&). In magnetic pyrochlores, the newly reported weak spin freezing near PRESERVED_PLACEHOLDER_^^^^4all:\44^^^^7 requires confirmation by local probes and broader frequency windows (&&&^^^^4all:\4^^^^&&&). In quantum implementations, robustness beyond closed-system or numerically modeled conditions remains contingent on decoherence, drive inhomogeneity, and higher-order corrections (Krithika et al., 2020).

A plausible implication is that freezing-induced interaction engineering should be understood not as a single mature discipline but as a cross-domain methodological motif. What unites the examples is the controlled use of freezing, freezing-front motion, premelting, or dynamical freezing to create interactions that are absent, weak, or inaccessible in the unfrozen state.